Analysis of junction conditions in optimal aeroassisted orbital plane change

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The atmospheric pass of the optimal heating-rate constrained aeroassisted orbital plane-change problem is considered. The problem formulation includes the thrust magnitude as a control variable. The junction conditions are the optimality conditions that must be satisfied by every pair of adjoining subarcs of the optimal trajectory. An analysis of these junction conditions shows that a number of prior assumptions on concatenating optimal subarcs must be revised. This is because the Hamiltonian of the problem is no longer regular due to the inclusion of thrust magnitude as a control variable. Necessary conditions for jump discontinuities in the angle of attack and thrust control are derived. We show that these necessary conditions permit a nontangential entry. Our conditions also show that a number of extremals hitherto not considered in the literature should be included in the construction of the switching structure. In addition, a number of new junction conditions are derived that may be used by numerical analysts to validate their codes. One interesting consequence of our analysis is a demonstration of the dual relationship between singular points and touch points.

Original languageEnglish
Pages (from-to)124-129
Number of pages6
JournalJournal of Guidance, Control, and Dynamics
Volume23
Issue number1
DOIs
Publication statusPublished - 2000 Jan 1

Fingerprint

thrust
orbitals
Hamiltonians
Angle of attack
Heating rate
Necessary Conditions
Optimal Trajectory
discontinuity
Demonstrations
Optimality Conditions
Singular Point
trajectory
Trajectories
thrust control
heating
Heating
Discontinuity
Jump
Inclusion
Attack

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Space and Planetary Science
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

@article{5e5b5e3468684945adfaf64b4b984310,
title = "Analysis of junction conditions in optimal aeroassisted orbital plane change",
abstract = "The atmospheric pass of the optimal heating-rate constrained aeroassisted orbital plane-change problem is considered. The problem formulation includes the thrust magnitude as a control variable. The junction conditions are the optimality conditions that must be satisfied by every pair of adjoining subarcs of the optimal trajectory. An analysis of these junction conditions shows that a number of prior assumptions on concatenating optimal subarcs must be revised. This is because the Hamiltonian of the problem is no longer regular due to the inclusion of thrust magnitude as a control variable. Necessary conditions for jump discontinuities in the angle of attack and thrust control are derived. We show that these necessary conditions permit a nontangential entry. Our conditions also show that a number of extremals hitherto not considered in the literature should be included in the construction of the switching structure. In addition, a number of new junction conditions are derived that may be used by numerical analysts to validate their codes. One interesting consequence of our analysis is a demonstration of the dual relationship between singular points and touch points.",
author = "Park, {Sang Young}",
year = "2000",
month = "1",
day = "1",
doi = "10.2514/2.4496",
language = "English",
volume = "23",
pages = "124--129",
journal = "Journal of Guidance, Control, and Dynamics",
issn = "0731-5090",
publisher = "American Institute of Aeronautics and Astronautics Inc. (AIAA)",
number = "1",

}

Analysis of junction conditions in optimal aeroassisted orbital plane change. / Park, Sang Young.

In: Journal of Guidance, Control, and Dynamics, Vol. 23, No. 1, 01.01.2000, p. 124-129.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Analysis of junction conditions in optimal aeroassisted orbital plane change

AU - Park, Sang Young

PY - 2000/1/1

Y1 - 2000/1/1

N2 - The atmospheric pass of the optimal heating-rate constrained aeroassisted orbital plane-change problem is considered. The problem formulation includes the thrust magnitude as a control variable. The junction conditions are the optimality conditions that must be satisfied by every pair of adjoining subarcs of the optimal trajectory. An analysis of these junction conditions shows that a number of prior assumptions on concatenating optimal subarcs must be revised. This is because the Hamiltonian of the problem is no longer regular due to the inclusion of thrust magnitude as a control variable. Necessary conditions for jump discontinuities in the angle of attack and thrust control are derived. We show that these necessary conditions permit a nontangential entry. Our conditions also show that a number of extremals hitherto not considered in the literature should be included in the construction of the switching structure. In addition, a number of new junction conditions are derived that may be used by numerical analysts to validate their codes. One interesting consequence of our analysis is a demonstration of the dual relationship between singular points and touch points.

AB - The atmospheric pass of the optimal heating-rate constrained aeroassisted orbital plane-change problem is considered. The problem formulation includes the thrust magnitude as a control variable. The junction conditions are the optimality conditions that must be satisfied by every pair of adjoining subarcs of the optimal trajectory. An analysis of these junction conditions shows that a number of prior assumptions on concatenating optimal subarcs must be revised. This is because the Hamiltonian of the problem is no longer regular due to the inclusion of thrust magnitude as a control variable. Necessary conditions for jump discontinuities in the angle of attack and thrust control are derived. We show that these necessary conditions permit a nontangential entry. Our conditions also show that a number of extremals hitherto not considered in the literature should be included in the construction of the switching structure. In addition, a number of new junction conditions are derived that may be used by numerical analysts to validate their codes. One interesting consequence of our analysis is a demonstration of the dual relationship between singular points and touch points.

UR - http://www.scopus.com/inward/record.url?scp=0033874372&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033874372&partnerID=8YFLogxK

U2 - 10.2514/2.4496

DO - 10.2514/2.4496

M3 - Article

AN - SCOPUS:0033874372

VL - 23

SP - 124

EP - 129

JO - Journal of Guidance, Control, and Dynamics

JF - Journal of Guidance, Control, and Dynamics

SN - 0731-5090

IS - 1

ER -